Moment-flux models for bacterial chemotaxis in large signal gradients

Abstract

Chemotaxis is a fundamental process in the life of many prokaryotic and eukaryotic cells. Chemotaxis of bacterial populations has been modeled by both individual-based stochastic models that take into account the biochemistry of intracellular signaling, and continuum PDE models that track the evolution of the cell density in space and time. Continuum models have been derived from individual-based models that describe intracellular signaling by a system of ODEs. The derivations rely on quasi-steady state approximations of the internal ODE system. While this assumption is valid if cell movement is subject to slowly changing signals, it is often violated if cells are exposed to rapidly changing signals. In the latter case current continuum models break down and do not match the underlying individual-based model quantitatively. In this paper, we derive new PDE models for bacterial chemotaxis in large signal gradients that involve not only the cell density and flux, but also moments of the intracellular signals as a measure of the deviation of cell’s internal state from its steady state. The derivation is based on a new moment closure method without calling the quasi-steady state assumption of intracellular signaling. Numerical simulations suggest that the resulting model matches the population dynamics quantitatively for a much larger range of signals.

Keywords

Chemotaxis Large signal gradient Derivation of PDE models

Mathematics Subject Classification

Notes

Acknowledgments

The authors would like to thank Professor Hans G. Othmer from University of Minnesota and Professor Radek Erban from University of Oxford for insightful discussions during the early stage of this project. This research was supported by NSF DMS-1312966 and NSF CAREER Award 1553637 to CX. CX was also supported by the Mathematical Biosciences Institute as a long-term visitor.